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Question Number 208277 by Mastermind last updated on 10/Jun/24

	Answered by Rasheed.Sindhi last updated on 10/Jun/24

	$\| \begin{matrix} 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 5 & 2 & 1 \\ 1 & 5 & 2 & 0 & 0 \\ 1 & 2 & 0 & 2 & 0 \\ 3 & 1 & 0 & 0 & 2 \end{matrix} \|$ $R_{2} = R_{2} - 2 R_{1}$ $= \| \begin{matrix} 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 3 & 0 & - 5 \\ 1 & 5 & 2 & 0 & 0 \\ 1 & 2 & 0 & 2 & 0 \\ 3 & 1 & 0 & 0 & 2 \end{matrix} \|$ $R_{4} = R_{4} - 2 R_{1}$ $= \| \begin{matrix} 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 3 & 0 & - 5 \\ 1 & 5 & 2 & 0 & 0 \\ 1 & 2 & - 2 & 0 & - 6 \\ 3 & 1 & 0 & 0 & 2 \end{matrix} \|$ $= - (1) \| \begin{matrix} 0 & 0 & 3 & - 5 \\ 1 & 5 & 2 & 0 \\ 1 & 2 & - 2 & - 6 \\ 3 & 1 & 0 & 2 \end{matrix} \|$ $R_{3} - R_{2}, R_{4} - 3 R_{2}$ $= - \| \begin{matrix} 0 & 0 & 3 & - 5 \\ 1 & 5 & 2 & 0 \\ 0 & - 3 & - 4 & - 6 \\ 0 & - 14 & - 6 & 2 \end{matrix} \|$ $= - (- 1) \| \begin{matrix} 0 & 3 & - 5 \\ - 3 & - 4 & - 6 \\ - 14 & - 6 & 2 \end{matrix} \|$ $= \| \begin{matrix} 0 & 3 & - 5 \\ - 3 & - 4 & - 6 \\ - 14 & - 6 & 2 \end{matrix} \|$ $= - 3 \| \begin{matrix} - 3 & - 6 \\ - 14 & 2 \end{matrix} \| - 5 \| \begin{matrix} - 3 & - 4 \\ - 14 & - 6 \end{matrix} \|$ $= - 3 (- 6 - 84) - 5 (18 - 56)$ $= - 3 (- 90) - 5 (- 38)$ $= 270 + 190 = 460$
	Commented by Mastermind last updated on 10/Jun/24

	$Thank you so much, I really appreciate .$
	Answered by Rasheed.Sindhi last updated on 10/Jun/24

	$\| \begin{matrix} 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 5 & 2 & 1 \\ 1 & 5 & 2 & 0 & 0 \\ 1 & 2 & 0 & 2 & 0 \\ 3 & 1 & 0 & 0 & 2 \end{matrix} \|$ $R_{3} - R_{4}, R_{5} - 3 R_{4}$ $= \| \begin{matrix} 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 5 & 2 & 1 \\ 0 & 3 & 2 & - 2 & 0 \\ 1 & 2 & 0 & 2 & 0 \\ 0 & - 5 & 0 & - 6 & 2 \end{matrix} \|$ $= - 1 \| \begin{matrix} 0 & 1 & 1 & 3 \\ 0 & 5 & 2 & 1 \\ 3 & 2 & - 2 & 0 \\ - 5 & 0 & - 6 & 2 \end{matrix} \|$ $C_{2} - C_{3}, C_{4} - 3 C_{3} 0 - 3 - 4 - 6 - 5$ $= - 1 \| \begin{matrix} 0 & 0 & 1 & 0 \\ 0 & 3 & 2 & - 5 \\ 3 & 4 & - 2 & ? 6 \\ - 5 & 6 & - 6 & 20 \end{matrix} \|$ $= - \| \begin{matrix} 0 & 3 & - 5 \\ 3 & 4 & ? 6 \\ - 5 & 6 & 20 \end{matrix} \|$ $= - [- 3 \| \begin{matrix} 3 & 6 \\ - 5 & 20 \end{matrix} \| - 5 \| \begin{matrix} 3 & 4 \\ - 5 & 6 \end{matrix} \|]$ $= 3 (60 + 30) + 5 (18 + 20)$ $= 270 + 190 = 460$
	Commented by Mastermind last updated on 10/Jun/24

	$Thank you so much, I really appreciate .$
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